text: A key choice that must be made is how many atoms to explicitly include in ones calculation.   In Big-O notation, calculations general scale as O(N3) where N is the number of combined ions and valence electrons.  For structure calculations, it is generally desirable to choose the smallest number of ions that can represent the structure.  For example, NaCl is a bcc cubic structure.  At a first guess, one might construct a cell of two interlocked cubes – 8 Na and 8 Cl – as ones unit cell.  This will give the correct answer but is computationally wasteful.  By choosing appropriate coordinates, one might simulate it with just two atoms: 1 Na and 1 Cl.
  Crystal structure calculations rely on periodic boundary conditions.  That is, the assumption is that the cell you have chosen is in the midst of an infinite lattice of identical cells.  By taking our 1 Na 1 Cl cell and copying it many times along each of the crystal axes, we will have simulated the same superstructure as our 8 Na 8 Cl cell but with much reduced computational cost.